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Newton's third law problem.
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electrodacus:

--- Quote from: AndyBeez on November 23, 2022, 05:23:01 pm ---And if you're using a hydrofoil, you can do it faster than the wind is blowing at you. Wrong but true. Google America's Cup. On the subject of friction reduction, is anyone using the downward force of gravity g in their equations? Does this thing still work in microgravity?

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Yes you can because you are allowed to change direction and thus take advantage of the vehicle kinetic energy.
An ideal setup where you sail perpendicular to wind direction can get the vehicle at any speed say 3x the wind speed then all you need to do is change direction to either direct upwind or direct downwind and since there is no friction loss in an ideal set up maintain that 3x speed forever.
In real world you can do the same but you need to repeat the change in direction as the stored kinetic energy will be used up to counter the losses.
IanB:

--- Quote from: electrodacus on November 23, 2022, 04:49:34 pm ---And my best example of what happens and it is measured in reality was the one about the power needed to overcome drag (same equation) is the same for a vehicle driving at 30m/s with no wind as it is for the same vehicle driving at 10m/s with a 20m/s head wind.
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And by extension a vehicle traveling at 0 m/s with a 30 m/s head wind...
electrodacus:

--- Quote from: IanB on November 23, 2022, 05:29:58 pm ---And by extension a vehicle traveling at 0 m/s with a 30 m/s head wind...

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Exactly right.
There is potential power available just not used by vehicle if it is anchored to earth but if it is not then that power will be accelerating that vehicle in the same direction as the wind.
So after 1ms of this the vehicle speed will no longer be zero but some value that can be calculated based on vehicle weight and friction losses as you calculate the gained kinetic energy and from that you can find out the new vehicle speed.
You will need to integrate as the wind speed relative to vehicle changes as the vehicle speed increases.
Nominal Animal:

--- Quote from: fourfathom on November 23, 2022, 04:26:11 pm ---So it all goes back to the original propeller/wheel vehicle that violates electro's misunderstood laws of physics.
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I see.  Thanks for letting me know!

This reminds me of the simple thought experiment on conservation of momentum and kinetic energy in elastic collisions.

Let's say you have a spaceship of mass M traveling at velocity V.  There is a projectile of mass m and velocity v on the same trajectory (v > V, both in the same exact direction).  They impact, but elastically, so that neither deforms, they just bounce without any losses.  What are the resulting velocities V' and v'?

Conservation of momentum says that MV + mv = MV' + mv'.  In a perfectly elastic collision, kinetic energy is also conserved, MV^2/2 + mv^2/2 = MV'^2/2 + mv'^2/2.  Solving the system of two equations for V' and v' yields two answers: one is V'=V, v'=v, i.e. no change.  The other is V' = (2mv+MV-mV)/(m+M), v' = (2MV+mv-Mv)/(m+M).  (Feel free to check, e.g. here.)

What happens when the projectile goes twice as fast as the ship, and weighs twice as much as the ship, i.e. m=2M, v=2V?

You work out the math, and out comes the unintuitive but physically correct and easily verifiable (using e.g. an air track) V'=7/3V≃2.333V, v'=4/3V≃1.333V.
In other words, the projectile loses one third of its velocity, and the ship gains four thirds; and the ship will end up traveling faster than the incoming projectile originally was.

If the velocities are a significant fraction of light speed, then one needs to switch to generalized momentum, (Newtonian momentum multiplied by the Lorentz factor γ, p = γmv) and relativistic kinetic energy (E=(1-γ)mc²) that are conserved, but at v<<c, the two yield the same answer to within rounding error.

This also answers the question, "Can you accelerate a spaceship to a velocity higher than at which you can lob boulders at it?", with "Yes.  Just use boulders with more mass than the ship has."

This is also the reason why one wants solar sails to be reflective, and not absorb the photons.  If the solar sail absorbs the photon, the craft gains the momentum of the photon.  However, if the solar sail reflects the photon, the craft gains up to two times the momentum of the original photon, depending on the angle of reflection, with maximum achieved when the photon is reflected back the way it came from.
electrodacus:

--- Quote from: Nominal Animal on November 23, 2022, 10:38:21 pm ---
This reminds me of the simple thought experiment on conservation of momentum and kinetic energy in elastic collisions.


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Elastic collisions is what you have between the air particles and the vehicle and that is how kinetic energy is transferred from the air molecules to the vehicle.
All the kinetic energy of the air molecule will end up transferred to the vehicle because it will in average bounce back and forth between the air molecule in the back and the vehicle body.

That is how you get to the wind power equation that I always mention as best case wind power available to any wind powered vehicle.
In that equation you have the air density about 1.2kg/m^2 the aerodynamic drag and projected surface area of the vehicle and the vehicle and wind speed.
Nothing else is needed to know what is available in ideal case to accelerate the vehicle.

So wind powered vehicle can be wind powered only in the stationary to wind speed region in the same direction.
You have the max available wind power when wind speed relative to vehicle is highest so stationary or traveling perpendicular to wind direction.
And zero wind power is available for a vehicle with any design traveling at the same speed as wind since air molecules can no longer collide with the vehicle to provide the increase in kinetic energy.

Vehicle can take energy from the wheel but that will result in a proportional reduction in vehicle kinetic energy so speed and appling that energy extracted at the wheel to another wheel or propeller or any other form of propulsion can not give a net gain even in ideal case.
Thus the only option to exceed wind speed directly down wind or drive directly upwind is to use energy storage.
Exceeding wind speed at an angle to wind direction is possible because there is still wind relative to vehicle and the only limitation when perpendicular to wind direction are the frictional losses.     
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